To evaluate the equation \( (8 - \sqrt{4}) - 24 \cdot (8 - \sqrt{16}) = 8 - 48 \), let's simplify both sides step by step.
First, simplify \( \sqrt{4} \) and \( \sqrt{16} \):
- \( \sqrt{4} = 2 \)
- \( \sqrt{16} = 4 \)
Now, substitute these values into the equation:
- Left Side:
\[
(8 - 2) - 24 \cdot (8 - 4)
\]
Simplifying further:
\[
6 - 24 \cdot 4 = 6 - 96 = -90
\]
- Right Side:
\[
8 - 48 = -40
\]
Now, we compare both sides:
- Left Side: \(-90\)
- Right Side: \(-40\)
Since \(-90 \neq -40\), the equation is **false**.
Therefore, the correct response would be:
**False, because the exponents should be added rather than multiplied.** (Note: This statement is somewhat misleading; the main issue here is that both sides do not equal, not necessarily about exponents in this specific case, so the reasoning is slightly off, but it denotes falsehood.)